Linear Algebra in the vector space of intervals

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Linear Algebra in the vector space of intervals
In a previous paper, we have given an algebraic model to the set of intervals. Here, we apply this model in a linear frame. For example, we define a notion of diagonalization of square matrices whose coefficients are intervals. But in this case, with respect to the real case, a matrix of order n could have more than n eigenvalues (the set of intervals is not factorial). But we define a notion of central eigenvalues this permits to describe criterium of diagonalization. We end this paper with the notion of Exponential mapping. 1 The associative algebra IR In [1], we have given a representation of the set of intervals in terms of associative algebra. More precisely, we define on the set IR of intervals of R a R-vector space structure. Next we embed IR in a 4dimensional associative algebra. This embedding permits to describe a unique distributive multiplication which contains all the possible results of the usual product of intervals. Recall that this usual product is not distributive wi...
Nicolas Goze
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2010
Where CORR
Authors Nicolas Goze
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